# Nonnegative matrix factorization

### From Wikimization

(Difference between revisions)

m (Reverted edits by 41.190.16.17 (Talk); changed back to last version by Ranjelin) |
m (Protected "Nonnegative matrix factorization" [edit=autoconfirmed:move=autoconfirmed]) |

## Revision as of 04:24, 17 February 2010

Exercise from Convex Optimization & Euclidean Distance Geometry, ch.4:

Given rank-2 nonnegative matrix

find a nonnegative factorization by solving

which follows from the fact, at optimality,

Use the known closed-form solution for a direction vector to regulate rank (rank constraint is replaced) by Convex Iteration;

set to a nonincreasingly ordered diagonalization and , then

In summary, initialize then alternate solution of

with

Global convergence occurs, in this example, in only a few iterations.